To expand the expression $(2x - 5)(x + 1)$, we will utilize the distributive property, which involves multiplying each term in the first bracket by each term in the second bracket. This method is commonly known as the FOIL method, an acronym that stands for First, Outer, Inner, and Last.

Let’s break down the expansion step by step:

1. First: Multiply the first terms from each bracket:

   $$2x \times x = 2x^2$$

2. Outer: Multiply the outer terms from the brackets:

   $$2x \times 1 = 2x$$

3. Inner: Multiply the inner terms from the brackets:

   $$-5 \times x = -5x$$

4. Last: Multiply the last terms from each bracket:

   $$-5 \times 1 = -5$$

Now, we combine all these products together:

Next, we simplify the expression by combining like terms. The like terms in this case are $2x$ and $-5x$:

Thus, the expanded form of $(2x - 5)(x + 1)$ is